MAT7102 Computing and Programming for Research

This course deals with the use of computer softwares in numerical computing, simulations, data analysis, research and provides analytical solution to the equations involved in physical sciences. It also numerically solves the equations; simulate the problems on a computer, for example, using Monte Carlo or molecular dynamics approach and make experimental observations and do theoretical modeling.
To train students who are able to use computers effectively in research and provide an in-depth knowledge of numerical techniques involved in data analysis.

Course objectives 
At the end of the course, the students should be able to:

• Solve equations numerically and simulate mathematical problems on computer
• Understand the different statistical tools, computing softwares and related application procedures
• Write interpretations and derive conclusions from computing, simulations and statistical analysis
• Acquire basic computing skills to manipulate data with ease while using any of studied mathematical packages
• Apply standard techniques to analyze and interpret key properties of algorithms used in computer programming.
• Use C++ programming language to solve mathematical problems
• Describe and work with iterative method for both linear and non-linear systems
• Describe optimization problems and use Eigen value in solving systems
• Describe numerical methods for solving ODEs and PDEs
• Work with boundary value problems
• Describe Finite Volume problems

Expected learning outcomes
By the end of this course learners are expected to:

• Analyze in depth the convergence properties of advanced iterative methods
• Implement and apply advanced iterative methods to solve linear and nonlinear problems
• Analyze in depth the convergence and stability properties of advanced time-stepping methods
• Conduct thorough error analysis and provide exact analytical solution of equations involved 
• Implement and apply time-stepping methods to solve ODE's and time-dependent PDE's including boundary value problems
• Do computations for their own research (simulations), implement methodology to help with our research
• Interact with scientists using complex data from diverse sources
• Disseminate new statistical methods as software
• Understand, critically appreciate and exploit new technologies as they emerge to allow us to do new types of data analysis.
• Use and understand the basics of operating systems, preparing presentations using power point beamer to mention but a few